Seismic data acquisition using an air gun source array and streamer are depicted in FIG. 1. At each source location, the air guns in the air gun array 11 are activated and inject a pulse of high pressure air into the water. The acoustic signals created by these high pressure air impulses travel through the water and the earth and are received by seismic detectors in the streamer cable 12. The acoustic signals arriving at the seismic detectors in the streamer cable are a summation of energy 13 that has traveled directly through the water, energy reflected (not shown) from the ocean surface 15, energy 14 reflected/refracted from the ocean bottom 16, and energy reflected/refracted from acoustic impedance changes in the earth's subsurface (not shown).
It has long been recognized that an estimate of the seismic source's far-field signature is required to correctly recover the acoustic impedance changes. U.S. Pat. No. 3,866,161 to Barr and U.S. Pat. No. 3,592,286 to Johnson are early attempts to acquire estimates of the source signature. Later attempts at source signature estimation are illustrated by U.S. Pat. Nos. 4,476,550, 4,476,553, 4,644,507, 4,868,794, and 6,081,765, all to Ziollowski; U.S. Pat. No. 4,908,801 to Bell; and U.S. Patent Application No. 2010/0002539 by Kragh, all patents utilizing near-field hydrophones. Other methodologies used to estimate seismic source signatures are U.S. Pat. No. 4,658,384 to Dragoset, involving placement of a single detector in a circle of air guns; U.S. Pat. No. 4,648,080 to Hargreaves, involving use of a short streamer in the mid-field; U.S. Pat. No. 4,694,435 to Magneville and U.S. Pat. No. 6,256,589 to Guimaraes, both involving use of a vertical cable; U.S. Pat. No. 6,018,765 to Laws, involving use of a detector placed in the mid-field; and U.S. Pat. No. 7,440,357 to Hopperstad, involving utilizing near-field detectors and ocean bottom reflections.
Most of the methods described by these patents generate the desired far-field source signature estimate from near-field or mid-field measurements. The sensors in a typical streamer cable are normally in the far field. Typically the distance between the center of an air gun array and the center of the first streamer section is on the order of 100 to 150 m. For typical air gun array dimensions of 16 m by 15 m, the sections at the head of the streamer are in the far-field excepting possibly the first few sections. As noted by the Barr patent, and by Kravis (“Estimation of Marine Source Signatures from Direct Arrivals to Hydrophone Groups,” Geophysical Prospecting 33, 987-998 (1985)), the spatial extent of a typical seismic air gun array is comparable to the wavelengths of the acoustic signals generated by the array of air guns. This spatial extent causes any measured source signature to be a function of the detector's distance from the air gun array and the detector's three-dimensional orientation with respect to the location of the air gun array.
There is no single definition for when a receiver is in the source's far field. Some working definitions include the following.                1. A receiver is in the far field when the character/shape of the measured signature is approximately constant with respect to the location of the center of the energy source. Once a signature is in the far-field, its amplitude is reduced as a function of the distance between the source's location and the measurement location; but the character/shape of the signature is constant.        2. Hargreaves (U.S. Pat. No. 4,648,080) uses that distance between a source array and a receiver at which the travel time difference due to travel path angularity between the extremities of the array and the receiver become insignificantly different from that which would be observed if the receiver were at infinity.        3. Laws (U.S. Pat. No. 6,081,765) uses D2/λ to estimate a minimum separation from the source, where D is the dimension of the source and λ is the wavelength.        4. Dragoset (U.S. Pat. No. 4,658,384) defines it as a distance from the source array such that the travel time from all the sources is effectively equal, e.g. ≈2 to 5 ms.        5. For typical tow depths of 5 to 15 m, a receiver may be considered to be in the far field if the measurement point is 5 to 10 times the maximum dimension of the source array.        
The tacit assumption is that the source generates a plane wave, so a far-field source signature estimate is really a far-field, zero incident angle signature. Current practice in seismic data processing is the assumption that a field record is the convolution of the source far-field signature with a time series that is the acoustic impedance of the earth. To recover the earth's acoustic impedance, the source signature must be removed from the recorded seismic trace (i.e. to designature a seismic trace). Poor estimates of the source signature leave artifacts in the seismic data that reduce the interpretability of the seismic section.
As described in Barr's U.S. Pat. No. 3,866,161, the desired vertical, far-field source signature can be measured directly by placing a detector at great depth below the air gun array. For typical air gun array depths on the order of 10 m, the far-field detector would need to be at a depth of approximately 300 m or more to be in the far-field and would need an additional 150 m or more of water below the far-field detector to generate a far-field estimate with a duration of 200 ms. As noted in many of the patents, this deep water requirement can add significant cost to a seismic survey. Additionally the need to locate in three dimensions both the air gun array, which is being towed through the water, and the far-field detector, which is typically stationary, increases the technical challenges with a subsequent increase in cost.
Because of the expense and technical complexity associated with measuring a far-field signature for each seismic survey, normal practice is to create air gun source signature estimates via air gun modeling programs. These programs provide source signature estimates such as the signatures shown in FIGS. 2 and 3. The primary differences between these two source signature estimates are the duration of the initial energy and the simplicity of the total signature. One measure of the compactness and simplicity of an air gun array signature is the signature's peak to bubble ratio, “PBR.” This is the ratio of the amplitude of the initial peak to the peak amplitude of the bubble. Well-tuned air gun arrays have PBRs greater than 25 which provide source signatures with durations of 50 ms to 100 ms. With the short duration and high amplitude of a high-PBR source signature, neglecting the energy in the bubble does not seriously impact the quality of the final seismic imaging and data analysis.
In an attempt to increase the low frequency content of the air gun signatures, the depth of the air gun arrays has been increased, larger gun volumes have been substituted for smaller gun volumes, and the diversity of the gun volumes has been reduced. These actions have decreased the PBRs and increased the effective duration of the source signature from tens of milliseconds to hundreds of milliseconds. The increases in signature complexity and duration can be seen by comparing FIG. 2 to FIG. 3. The increased amplitude of the bubble train energy means that the designature processing must include the bubble train. For low PBR source signatures, not including the bubble train energy in the designature process effectively increases the noise floor in the final seismic image.
An unintended consequence of reducing the PBR is a reduction in the accuracy of the modeled source signature estimate. FIG. 4 compares the measured near-field signature with the modeled near-field signature for three gun volumes. The modeled air gun signatures provide a good estimate of the amplitude of the initial peak and a good estimate of the time the peak of the first bubble occurs. What the modeled signatures do not provide is a good estimate of the air gun bubble train. Consequently with deeper tow depths, as the peak to bubble ratio of an air gun source drops below 25 to 1, the modeled source signature estimate becomes less reliable.
The reliability of the source signature estimate is further reduced if the frequencies of interest are below 30 Hz. The decrease in signature reliability arises because a considerable amount of the energy below 20-30 Hz may be contained within the air gun bubble. The energy in the bubble train is significant for low PBR source arrays, since in geologic settings where there is strong overburden scattering and/or attenuation, the low frequency component (<30 Hz) is often the primary useable energy band. The obvious solution to an unreliable modeled source signature estimate is to measure the source signature. As noted in the previously cited patents, measured source signature estimates are acquired by 1) directly measuring the source signature using a deep tow sensor, 2) forming an extrapolation of near-field measurements, 3) towing a mini-streamer below and within the near-field of the air gun array, and 4) extracting an estimate of the source signature from the bottom arrivals. All of these methods of estimating a source's signature are either expensive or difficult to implement, or provide poor or contaminated estimates of the source signature. What is needed is a method that can provide a usable estimate of an air gun array's signature when modeling and other signature estimation techniques do not provide acceptable results.